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A353187 Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive terms contains only one pair that is not coprime.

%I A353187 #36 Feb 22 2023 14:59:03
%S A353187 1,2,4,5,6,8,11,12,14,17,18,20,23,24,26,29,30,32,37,38,40,41,42,44,47,
%T A353187 48,50,53,54,56,59,60,62,67,68,70,71,72,74,77,78,80,83,84,86,89,90,92,
%U A353187 97,98,100,101,102,104,107,108,110,113,114,116,119,120,122,127,128,130,131
%N A353187 Lexicographically earliest strictly increasing sequence of positive integers in which every triple of consecutive terms contains only one pair that is not coprime.
%C A353187 Based on testing the first 1000 primes of the form 3n-1, it seems that A003627 is a subsequence.
%H A353187 Ivan N. Ianakiev, <a href="/A353187/b353187.txt">Table of n, a(n) for n = 1..10000</a>
%t A353187 next[n_,m_]:=Piecewise[{
%t A353187 {(k=m+1; While[!CoprimeQ[k,n]||!CoprimeQ[k,m],k++]; k),AllTrue[{n,m},EvenQ]},
%t A353187 {m+2,OddQ[n]&&EvenQ[m]},{m+1,EvenQ[n]&&OddQ[m]}}];
%t A353187 a[1]=1;a[2]=2;a[n_]:=a[n]=next[a[n-2],a[n-1]];a/@Range[100]
%o A353187 (PARI) { for (v=1, 122, if (v<=2 || ((gcd(pp,p)==1) + (gcd(p,v)==1) + (gcd(v, pp)==1))==2, print1 (v", "); [pp,p]=[p,v])) } \\ _Rémy Sigrist_, May 01 2022
%Y A353187 Cf. A047255.
%K A353187 nonn
%O A353187 1,2
%A A353187 _Ivan N. Ianakiev_, Apr 29 2022